This document provides an overview of key capital budgeting concepts like internal rate of return (IRR), net present value (NPV), and modified internal rate of return (MIRR). It defines IRR as the discount rate at which NPV equals zero and explains that multiple IRRs can exist. It also discusses limitations of IRR and defines MIRR as an improved method that uses different rates for financing and reinvesting cash flows. The document uses examples to illustrate concepts of NPV, IRR, multiple IRRs, and how MIRR addresses shortcomings of IRR.

1. A Brief introduction of current
issues in Capital Budgeting
Raman Kumar Sahu ,Nishant Rishav

2. CIL Guideline for Selection of
Projects
 IRR >= 12% at 85% capacity
utilization
 NPV >=0 at discounting rate =12%

3. What is IRR and NPV ?
 Internal Rate of Return (IRR) is
defined as the discounting rate at
which NPV of all cashflows is equal to
zero.
 Net Present Value(NPV)can be
defined as the difference between the
present value of all cash inflows and
the present value of all cash outflows.

4. Case Study : Actual data

5. EXAMPLE 1

6. PERIOD CASHFLOW1 CASHFLOW2
0 -100 -100
1 82 10
2 23 10
3 10 10
4 5 20
5 5 50
6 10 120
IRR 18% 18%
PROFIT 35 120
MIRR@8%,8% 11% 16%
compunding period RATE of reinvestment FV for CF1 FV for CF2
5 8% 120.4849023 14.69328077
4 8% 31.29124608 13.6048896
3 8% 12.59712 12.59712
2 8% 5.832 23.328
1 8% 5.4 54
0 8% 10 120
total FV 185.6052684 238.2232904
EXAMPLE 2

7. EXAMPLE 3

8. Multiple IRRs !
NPV vs Discount rate
Multiple IRR values
•2110.10%
•19.98%
•1.09%
Moreover, NPV is negative between
discounting rates 1.09% -19.98%.

9. Multiple IRRs !
Multiple IRR values
•1018.60%
•11.66%
•0.75%
Moreover, NPV is negative between
discounting rates 0.75% -11.66%.
NPV vs Discount rate

10. NPV vs Discount rate
HIRING OPTION DEPARTMENTAL OPTION
NPV at 12% 142550.89 Cr 157845.26 Cr
IRR 26.15 % 25.92 %

11. Back to Basics
 One of the most fundamental concepts in
finance is that money has a time value.
 A Rupee today is worth more than a
Rupee tomorrow.
 The reason is straightforward,ie, a Rupee
that you receive today can be used for
creating a value of more than a Rupee at
some future time.

12. NPV
•Net Present Value (NPV) is the difference between the ‘present
value’ of cash inflows and the ‘present value’ of cash outflows.
•NPV is used in capital budgeting to analyze the profitability of a
projected investment or project.
NPV = -C0 + C1/(1+r) + C2/(1+r)2 – C3/(1+r)3 + C4/(1+r)4 + C5/(1+r)5
where , Discounting all the cash flows at r % per annum.
Similarly, FV= C5 + C4(1+r) –C3(1+r)2 +C2(1+r)3 + C1(1+r)4 - C0 (1+r)5
Future value of all cash flows at the end of 5th year at r% per annum.

13. IRR
 IRR is the discounting rate for which NPV is equal to zero.
 Lets equate the expression for NPV to zero.
NPV = -C0 + C1/(1+r) + C2/(1+r)2 – C3/(1+r)3 + C4/(1+r)4 + C5/(1+r)5 =0
Rearranging the terms of the above equation gives us an equation of
form:
a0 + a1(1+r) -a2(1+r)2 +a3(1+r)3 + a4(1+r)4 - a5(1+r)5 =0
This is an equation of fifth order therefore can have a maximum number
of 5 real roots, hence a maximum of 5 IRRs possible.
• MS Excel returns only one positive value of IRR, hence sometimes the
other possible IRR values are left unreported in project reports.

14. Limitations of IRR
The first main issue with IRR is that multiple solutions can be
found for the same project.
The second problem is that the assumption that positive cash
flows are reinvested at the IRR gives an over-optimistic picture.
Often the option having lower IRR value has greater NPV at
12% discounting rate .

15. MIRR
 An improvement over the concept of IRR
 Modified internal rate of return is a solution to the shortcomings of
internal rate of return as a project evaluation technique.
 There are two major disadvantages of IRR.
 One is Multiple IRR and the other one is the impractical assumption
of reinvesting positive cash flows at the rate of project IRR.
 Modified internal rate of return (MIRR) assumes that positive cash
flows are reinvested at the firm's cost of capital, and the initial
outlays are financed at the firm's financing cost. By contrast, the
traditional IRR assumes the cash flow from a project are reinvested
at the IRR.
 FV of all inflows at reinvestment rate = (PV of all outflows at
finance rate)(1+MIRR)n
 In case of IRR, reinvestment rate and finance rate are same as IRR.
FV of all inflows at IRR rate = (PV of all outflows at IRR
rate)(1+IRR)n


16. Concepts of MIRR
Financerate 10%
Reinvestmentrate 10%
12.72%
Year Cashflow PV FV
0 -325000 -325000
1 87000 105270
2 -10000 -8264
3 372000 372000 PV 333264
-333264 477270 FV 477270
MIRRcalculatedfromexcelfunction
Thecalculationisasolutiontotwomajorproblemsthatexistwith
thepopularIRRcalculation.
1.ThefirstmainproblemwithIRRisthatmultiplesolutionscanbe
foundforthesameproject.
2.Thesecondproblemisthattheassumptionthatpositivecash
flowsarereinvestedattheIRRisconsideredimpracticalinpractice.
WiththeMIRR,onlyasinglesolutionexistsforagivenproject,and
reinvestmentrateofpositivecashflowsismuchmorevalidin
practice.

17. Final Comments
 MIRR presents a more realistic picture
of the project than IRR
 IRR should never be used in isolation
to determine the financial viability of
the project.
 IRR should be used in conjuction with
NPV.